All categories

3 years ago

HELP ASAP PLZ ITS URGENT

Mathematics

1 answer:

Radda [10]3 years ago

8 0

Answer:

It landed at a height of 14 feet

Step-by-step explanation:

Given

$y = -\frac{1}{8}x^2 +4x$ --- Path of a t-shirt

$3y = 2x - 14$ --- height of bleachers

Required

Height when t-shirts land in bleachers

$3y = 2x - 14$

Make y the subject

$y = \frac{2}{3}x - \frac{14}{3}$

Substitute $y = \frac{2}{3}x - \frac{14}{3}$ in $y = -\frac{1}{8}x^2 +4x$

$\frac{2}{3}x - \frac{14}{3} = -\frac{1}{8}x^2 +4x$

Multiply through by 24

$16x- 112 = -3x^2 +96x$

Express as:

$3x^2 + 16x -96x- 112 = 0$

$3x^2 -80x- 112 = 0$

Using a calculator:

$x = 28$ or $x = -\frac{4}{3}$

x can not be negative:

So:

$x = 28$

Substitute $x = 28$ in $y = -\frac{1}{8}x^2 +4x$ to calculate the height it landed

$y = -\frac{1}{8} * 28^2 + 4 * 28$

$y = 14$

You might be interested in

What is the area of a circle, if it's radius is 2cm?

slega [8]

25.13cm^2 or 8pi. The radius of a circle is 2 x pi x r^2. R is the radius. 2 x pi x 2^2cm -> 2 x pi x 4cm -> 8cm x pi -> 25.13cm^2. Leaving the answer in terms of pi would be 8pi.

8 0

3 years ago

Can someone please explain?

AlladinOne [14]

<h2>Hello!</h2>

The answer is:

The correct option is the first option:

$y=-4x+64$

To write the equation of the line in slope-interception form we need to extract all the information that we need from the graphic.

We must remember that the slope-interception form of the lines is:

$y=mx+b$

Where,

y, is the function

m, is the slope of the line

x, is the variable

b, is the y-axis intercept

We can find the slope using the following formula:

$m=\frac{ChangeInY}{ChangeInX}$

Which is for this case:

$m=\frac{64}{16}=4$

As we can see from the graphic, the line is decresing, so the sign of the slope "m" will be negative, so:

$m=-4$

We can find the value of "b" seeing where the line intercepts the y-axis.

As we can see it intercept the y-axis at: $y=64$

Then, now that we already know the value of "m" and "b", we can write the equation of the line:

$y=mx+b=-4x+64\\y=-4x+64$

So, the correct option is the first option:

$y=-4x+64$

Have a nice day!

4 0

3 years ago

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .