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3 years ago

Find the following measure for this figure.

Mathematics

2 answers:

Eva8 [605]3 years ago

8 0

Answer:

The correct answer is 5√146π square units

Step-by-step explanation:

From the figure we can see a cone

Points to remember

Lateral surface area of cone = πrl

r - Radius of cone

l - Slant height of cone

To find the slant height

From figure we get,

r = 5 units and height = 11 units

Slant height² = radius² + height² = 5² + 11² = 25 + 121 = 146

Slant height = √146 units

To find the lateral area

lateral area = πrl = π * 5 * √146 = 5√146π square units

The correct answer is 5√146π square units

ss7ja [257]3 years ago

4 0

Answer: last option (5π√146 units²)

Step-by-step explanation:

To solve the exercise you must apply the formula for calculate the lateral area of a cone, which is shown below:

$LA=r*L*\pi$

where r is the radius but L is the slant height.

As you can see in the figure attached:

$r=5$

But you need to find the slant height with the Pythagorean Theorem (L would be the hypotenuse):

$L=\sqrt{11^2+5^2}=\sqrt{146}$

Substitute into the formula, then:

$LA=(5)(\sqrt{146})\pi=5\pi\ \sqrt{146$ units²

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Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a rand

SOVA2 [1]

Answer:

Question 1:

(a) P(x<60) = 0.9236

(b) P(x>16) = 0.9564

(c) P(16<x<60) = 0.88

(d) P (x>60) = 0.0764

Question 2:

(a) P(x<3) = 0.0668

(b) P(x>7) = 0.0062

(c) P(3<x<7) = 0.927

Step-by-step explanation:

Question 1:

x = no. of mg of porphyrin per deciliter of blood.

μ = 40

σ = 14

(a) We need to compute P(x<60). We need to find the z-score using the normal distribution formula:

z = (x - μ)/σ

P(x<60) = P((x - μ)/σ < (60 - 40)/14)

= P(z < 20/14)

= P(z<1.43)

Using the normal distribution probability table we can find the value of p at z=1.43.

P(z<1.43) = 0.9236

so, P(x<60) = 0.9236

(b) P(x>16) = P(z>(16-40)/14)

= P(z>-1.71)

= 1 - P(z<-1.71)

= 1 - 0.0436

P(x>16) = 0.9564

(c) P(16<x<60) = P((16-40)/14) < x < (60-40)/14)

= P(-1.71 < z < 1.43)

This probability can be calculated as: P(z<1.43) - P(z<-1.71)

P(16<x<60) = 0.9236 - 0.0436

P(16<x<60) = 0.88

(d) P(x>60) = 1 - P(x<60)

we have calculated P(x<60) in part (a) so,

P(x>60) = 1 - 0.9236

P (x>60) = 0.0764

Question 2:

μ = 4.5 mm

σ = 1.0 mm

In this question, we will again compute the z-scores and then find the probability from the normal distribution table.

(a) P(x<3) = P(z<(3-4.5)/1)

= P(z<-1.5)

P(x<3) = 0.0668

(b) P(x>7) = 1 - P(x<7)

= 1 - P(z<(7-4.5)/1)

= 1 - P(z<2.5)

= 1 - 0.9938

P(x>7) = 0.0062

(c) P(3<x<7) = P(x<7) - P(x<3)

we have computed both of these probabilities in parts (a) and (b) so,

P(3<x<7) = 0.9938 - 0.0668

P(3<x<7) = 0.927

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If y varies directly as x^2 and y=12 when x=2, find y when x=5

Shkiper50 [21]

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Montano1993 [528]

The tangent line to y = f(x) at a point (a, f(a) ) has slope dy/dx at x = a. So first compute the derivative:

y = x² - 9x → dy/dx = 2x - 9

When x = 4, the function takes on a value of

y = 4² - 9•4 = -20

and the derivative is

dy/dx (4) = 2•4 - 9 = -1

Then use the point-slope formula to get the equation of the tangent line:

y - (-20) = -1 (x - 4)

y + 20 = -x + 4

y = -x - 24

The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is

y - (-20) = 1 (x - 4)

y + 20 = x - 4

y = x - 24

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