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3 years ago

Find the surface area of the prism. 10m 15m 16m 17m 17m

Mathematics

1 answer:

Alexeev081 [22]3 years ago

4 0

is it a rectangular prism

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Suppose Q is the midpoint of PR. Use the information to find the missing value.

murzikaleks [220]

Step-by-step explanation:

If Q is the midpoint of PR

Then PQ + QR = PR

(6x + 25) + (16 - 3x)

group the same terms and add them

(6x - 3x) + (25 + 16)

Hence PR = (3x + 41)

But to find the value of PR....If Q is the midpoint....then PQ = QR...since they are both half lengths of PR;

; 6x + 25 = 16 - 3x

; 6x + 3x = 16 - 25...;9x = -9

Hence the value of...x = -1

Then substitute the value of x into the equation of PR....3x + 41

;3(-1) + 41

;-3 + 41

Hence PR = 38

3 0

3 years ago

Read 2 more answers

The mean amount of money spent on lunch per week for a sample of 100 students is $21. If the margin of error for the population

Digiron [165]

From the given mean and margin of error, the 99% confidence interval for the mean amount of money spent on lunch per week for all students is:

[$19.5, $22.5].

<h3>How to calculate a confidence interval given the sample mean and the margin of error?</h3>

The confidence interval is given by the sample mean plus/minus the margin of error, hence:

The lower bound is the sample mean subtracted by the margin of error.

The upper bound is the sample mean added to the margin of error.

For this problem, we have that:

The sample mean is of $21.

The margin of error is of $1.50.

Hence the bounds are given as follows:

Lower bound: 21 - 1.50 = $19.50.

Upper bound: 21 + 1.50 = $22.50.

Hence the interval is [$19.50, $22.50].

More can be learned about confidence intervals at brainly.com/question/25890103

#SPJ1

7 0

1 year ago

Suppose r⃗ (t)=cos(πt)i+sin(πt)j+5tkr→(t)=cos(πt)i+sin(πt)j+5tk represents the position of a particle on a helix, where zz is th

gtnhenbr [62]

Answer:

a) t = 4

b) v = pi j + 5 k

c) rt = 1i + (pi t) j + (20 +5t )k

Step-by-step explanation:

You have the following vector equation for the position of a particle:

$r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}$ (1)

(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.

For a height of 20 you have:

$5t=20\\\\t=\frac{20}{5}=4$

(b) The velocity of the particle is the derivative, in time, of the vector position:

$v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}$ (2)

and for t=4 (height = 20):

$v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}$

(c) The vector parametric equation of the tangent line is given by:

$r_t(t)=r_o+vt$ (3)

ro: position of the particle for t=4

$r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}$

Then you replace ro and v in the equation (3):

$r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}$

3 0

4 years ago

If someone can answer all these ill give 100 points

Helga [31]

Answer:

1. x = -6

2. x = 2

3. x = 6

4. x = 3

5. x = -5

6. x = -1

7. x = 0

8. x = 9

9. x = -4

10. x = 7

Step-by-step explanation:

$-10x = -8x + 12$

$-10x+8x=-8x+12+8x$
$-2x=12$

$-2x/-2=12/-2$
$x=-6$

$9-5x+x=1-x+x$
$-4x+9=1$

$-4x+9-9=1-9$
$-4x=-8$

$-4x/-4=-8/-4$
$x=2$

$-2x+16-x=x-2-x$
$-3x+16=-2$

$-3x+16-16=-2-16$
$-3x=-18$

$-3x/3=-18/-3$
$x = 6$

$(-4)(6x)+(-4)(-2)= -8x-40$
$-24x+8=-8x-40$

$-24x+8+8x=-8x-40$
$-16x+8=-40$

$-16x+8-8=-40-8$
$-16x=-48$
$-16x/-16=-48/-16$
$x=3$

$37 - 8x = (-7)(x)+(-7)(-6)$
$-8x+37=-7x+42$
$-8x + 37 + 7x = -7x + 42 + 7x$
$-x+37=42$
$-x+37-37=42-37$
$-x=5$
$-x/-1=5/-1$
$x=-5$

$6x+(-2)(2)+(-2)(8x) = 10 + 4x$
$6x-4-16x = 10 + 4x$
$-10x - 4 = 4x + 10$
$-10x - 4 -4x=4x+10-4x$
$-14x-4=10$
$-14x-4+4=10+4$
$-14x=14$
$-14x/-14=14/-14$
$x=-1$

$(-2)(x) + (-2)(1) = (2)(x) + (2)(-1)$
$-2x-2=2x-2$
$-2x-2-2x = 2x - 2 - 2x$
$-4x - 2 = -2$
$-4x-2+2=-2+2$
$-4x=0$
$-4x/-4=0/-4$
$x=0$

$(-3)(x)+(-3)(3)=(-6)(x)+(-6)(-3)$
$-3x-9=-6x+18$
$-3x-9+6x=-6x+18+6x$
$3x-9=18$
$3x-9+9=18+9$
$3x=27$
$3x/3 = 27/3$
$x=9$

$6x-36=(-4)(-2x)+(-4)(7)$
$6x-36= 8x -28$
$6x-36-8x = 8x - 28 - 8x$
$-2x-36=-28$
$-2x-36+36=-28+36$
$-2x = 8$
$-2x/-2=8/-2$
$x=-4$

10.

$(2)(x)+(2)(1) = -2x + 30$
$2x+2=-2x+30$
$2x+2+2x=-2x+30+2x$
$4x+2=30$
$4x+2-2=30-2$
$4x=28$
$4x/4=28/4$
$x=7$

4 0

3 years ago

What is the value of x in the equation 3<br> X-<br> 3<br> 8<br> 5<br> X2

gizmo_the_mogwai [7]

Answer:

x = 1

Step-by-step explanation:

$\frac{1}{2} x - \frac{3}{4} = \frac{3}{8} - \frac{5}{8} x \\ \\ \frac{1}{2} x + \frac{5}{8} x = \frac{3}{8} + \frac{3}{4} \\ \\ \frac{1 \times 4}{2 \times 4} x + \frac{5}{8} x = \frac{3}{8} + \frac{3 \times 2}{4 \times 2} \\ \\ \frac{4}{8} x + \frac{5}{8} x = \frac{3}{8} + \frac{6}{8} \\ \\ \frac{4 + 5}{8} x = \frac{3 + 6}{8} \\ \\ \frac{9}{8} x = \frac{9}{8} \\ \\ x = \frac{9}{8} \times \frac{8}{9} \\ \\ x = 1$

8 0

3 years ago