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3 years ago

A circle with radius 3 has a sector with a central angle of 60. What is the area of the sector?

Mathematics

1 answer:

CaHeK987 [17]3 years ago

6 0

Answer:

Sector area = (central angle / 360) * PI * radius^2

Sector area = (1/6) * PI * 3^2

Sector area = 9/6 * PI

Sector area = 4.7123889804

Step-by-step explanation:

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Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xe^y + ye^z +

LUCKY_DIMON [66]

Answer:

$D_{\vec{u}}f(0,0,0)=\frac{6}{\sqrt{54}}$

Step-by-step explanation:

We need to find the directional derivative of the function at the given point in the direction of the vector v.

$f(x, y, z)=xe^{y} + ye^{z} + ze^{x}$ ,point (0, 0, 0) and $v=$

By Theorem: If f is a differentiable function of x , y and z , then f has a directional derivative for any unit vector $\overrightarrow{v} =$ and

$D_{\overrightarrow{u}}f(x,y,z)=f_{x}(x,y,z)u_1+f_{y}(x,y,z)u_2+f_{z}(x,y,z)u_3$

where $\overrightarrow{u}=\frac{\overrightarrow{v}}{||v||}$

since, $v=$

then $\overrightarrow{u}=\frac{\overrightarrow{v}}{||v||}$

$\overrightarrow{u}=< \frac{6}{\sqrt{6^{2}+3^{2}+(-3)^{2}}},\frac{3}{\sqrt{6^{2}+3^{2}+(-3)^{2}}},\frac{-3}{\sqrt{6^{2}+3^{2}+(-3)^{2}}} >$

$\overrightarrow{u}=< \frac{6}{\sqrt{54}},\frac{3}{\sqrt{54}},\frac{-3}{\sqrt{54}} >$

The partial derivatives are

$f_{x}(x,y,z)=e^{y}+ze^{x}$

$f_{y}(x,y,z)=xe^{y}+e^{z}$

$f_{z}(x,y,z)=ye^{z}+e^{x}$

Then the directional derivative is

$D_{\vec{u}}f(x,y,z)=(e^{y}+ze^{x})(\frac{6}{\sqrt{54}})+(xe^{y}+e^{z})(\frac{3}{\sqrt{54}})+(ye^{z}+e^{x})(\frac{-3}{\sqrt{54}})$

so, directional derivative at point (0,0,0)

$D_{\vec{u}}f(0,0,0)=(e^{0}+0e^{0})(\frac{6}{\sqrt{54}})+(0e^{0}+e^{0})(\frac{3}{\sqrt{54}})+(0e^{0}+e^{0})(\frac{-3}{\sqrt{54}})$

$D_{\vec{u}}f(0,0,0)=\frac{6}{\sqrt{54}}+\frac{3}{\sqrt{54}}+\frac{-3}{\sqrt{54}}$

$D_{\vec{u}}f(0,0,0)=\frac{6+3-3}{\sqrt{54}}$

$D_{\vec{u}}f(0,0,0)=\frac{6}{\sqrt{54}}$

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4 years ago

What is an equivalent fraction for 8/9

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16/18
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3 years ago

Read 2 more answers

If the P-value of a test of significance is greater than the level of significance, then which of these conclusions are appropri

VLD [36.1K]

Answer:

Step-by-step explanation:

In general, when the p-value is "high" (ie greater than or equal to the significance level), our sample results could have occurred by random chance alone when null hypothesis H0 is true. So we cannot reject H0 with high p-values. That doesn't mean we can accept H0 as being true. Statistical hypothesis testing is used to determine whether the result of a data set is statistically significant. This test provides a p-value, representing the probability that random chance could explain the result. In general, a p-value of 5% or lower is considered to be statistically significant. If the P-value is less, reject the null hypothesis. If the P-value is more, keep the null hypothesis. 0.003 < 0.05, so we have enough evidence to reject the null hypothesis and accept the claim.A null hypothesis is a hypothesis that says there is no statistical significance between the two variables in the hypothesis. ... In the example, Susie's null hypothesis would be something like this: There is no statistically significant relationship between the type of water I feed the flowers and growth of the flowers.

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4 years ago

25°c convert to ° f

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

i used google to answer it.

x - 32 * 5/9 =25

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3 years ago

Find the value of 14/8 + 15/12

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